1. Field of the Invention
The invention relates to a floating point processing unit and, more particularly, to a floating point processing unit which includes means for sequencing operands and results of simple and compound arithmetic operations to pipeline arithmetic operations performed by the floating point processing unit.
2. Description of Related Art
As is known in the art, a floating point number is comprised of an exponent portion and a mantissa portion. The exponent portion represents a power to which a base number such as 2 is raised and the mantissa portion is a number to be multiplied by the base. Accordingly, the actual number represented by a floating point number is the mantissa portion multiplied by the base number raised to a power specified by the exponent portion. In such a manner, any particular number may be approximated in floating point notation as f.times.B.sup.e or (f,e) where f is an n digit signed mantissa, e is an m digit signed integer exponent and B is the base number system used. For example, in many computer systems, the base number system used is the binary number system where B=2. Other computer systems use the decimal number system (B=10) or the hexadecimal number system (B=16) as their base number system.
Most floating point numbers may be characterized as either a normalized floating point number or a denormalized floating point number. A normalization scheme for floating point numbers assures that all floating point numbers with the same value have the same representation. One normalization scheme is to ensure that the position of the most significant bit of the mantissa is one. Accordingly, to normalize a floating point number, the binary point is shifted to the right until the left most digit in the mantissa has a value of one. The exponent is then decreased so that the value of the combination of the mantissa and the exponent remains constant. This procedure is often called "wrapping" because the exponent is often decreased until it "wraps" around zero and becomes negative.
Conversely, a floating point number which is not normalized is denormalized. Thus, in accordance with the normalization scheme set forth above, a floating point number whose leading significand bit is zero is a denormalized floating point number. To denormalize a normalized floating point number, the reverse procedure may be followed. Thus, a typical denormalization process is shifting the decimal point of the denormalized number to the left the desired amount and then increasing the exponent until the value of the combination of the mantissa and the exponent is the same.
Floating point numbers may be added, subtracted, multiplied, or divided. Floating point addition can only be performed, however, when the exponents of both input operands are the same. Hence, those operands input an add unit for addition or subtraction which have different exponents must be adjusted to make the exponents coincide. Adjustments to the exponents must be accompanied by shifts in the mantissa in order to keep the values of the operands the same. Typically, the necessary adjustment is made by denormalizing the smaller number. The sum or difference between two input operands may be a denormalized number, so that the add unit is typically associated with a renormalizer for normalizing results.
In a practical computer, however, arithmetic operations are often complicated by the fact that the mantissa portion of a number is not of infinite "precision", i.e. there are not an unlimited number of digits which may be assigned to the mantissa portion of a floating point number. Instead, floating point numbers are normally processed in a register comprising a fixed number of digits. Thus, although two input operands to be added together or subtracted from each other may be exact numbers, the sum or difference after completing the addition or subtraction operation may create more significant digits than the fixed number of digits in the register. As a result, an accurate representation of the sum or difference must be squeezed into the fixed number of digits in the register by the processes of normalizing and rounding.
The limitation that floating point numbers are never of infinite precision makes it very important that the input operands used in floating point multiplication or floating point division are normalized before performing the arithmetic operation. For example, if two floating points numbers, each having an eight bit mantissa, are multiplied together, the result will be a floating point number having a sixteen bit answer. Despite this increase in mantissa size, the number of bits in the output mantissa must be the same as the number of bits in the input mantissas. Thus, to form an output, half of the bits of the answer must be thrown away, typically by deleting the right most bits of the mantissa. If the input operands are not normalized, the answer will not be left justified and bits containing an important part of the answer will not be thrown away. If, on the other hand, the input operands are normalized, the answer will be left justified and as little information as possible will be thrown away when producing the output.
Two other problems arise when arithmetic operations are performed using a floating point processing unit. These are the conditions generally referred to as arithmetic "underflow" and arithmetic "overflow". There are two ranges of numbers that correspond to arithmetic overflow and arithmetic underflow, respectively. If the result of an arithmetic operation is greater than the largest positive or less than the least negative value representable, arithmetic overflow occurs. On the other hand, when the result of arithmetic operation is too small to be expressed, either positive or negative arithmetic underflow has occurred.
Overflow occurs whenever the destination formats largest finite number is exceeded in magnitude by what would have been the rounded floating point result. For example, in a floating point multiplication operation where the mantissas are multiplied and the exponents added, if the sum of the exponents exceeds the maximum representable exponent, an overflow has occurred. On the other hand, in a floating point division operation, if the divisor is sufficiently smaller than the dividend, the quotient may exceed the maximum number representable. This too, would be an overflow condition.
Conversely, two correlated events contribute to underflow. One event is the creation of a tiny, non-zero result which cannot be represented as a normalized number. Because it is so small, this number may cause some other exception later such as overflow upon division. The other event is extraordinary loss of accuracy during the approximation of such tiny numbers by denormalized numbers. While underflow and/or overflow conditions may occasionally be produced during addition or subtraction operations, they are most common during floating point multiplication or division operations.
To obtain the fastest possible computational throughput, digital computer architecture often employs pipeline processing techniques. The data to be processed is streamed through the pipeline, thereby obtaining faster processing by a factor that depends upon the number of pipeline stages utilized. Pipelined floating point processor units having multiple arithmetic operation units have been disclosed in the art. For example, U.S. Pat. No. 4,683,547 to DeGroot discloses a data processing system having a multiple floating point arithmetic unit with a putaway at a bypass bus. In the DeGroot apparatus, the results of each multiply/divide operation are passed on to a bypass bus to the input of an adder along with the inputs from the cumulate bypass bus which is the output from the adder for an automatic add operation on an accumulate multiply or accumulate divide operation. This configuration allows two floating point results be produced each cycle.
U.S. Pat. No. 4,075,704 to O'Leary discloses a floating point data processor comprising a floating point adder, a floating point multiplier and a plurality of memory register means. The floating adder individually drives a first bus for supplying selectable inputs to memory register means, the adder and the multiplier while the floating multiplier individually drives a second bus for also supplying selectable inputs to memory register means, the adder and the multiplier. The adder and the multiplier are provided with individual destination, input busses for receiving selectable outputs from memory register means. The floating adder and the floating multiplier are pipelined circuits each including a plurality of stages with intermediate temporary storage means for catching partial results computed during one clock period for presentation to the next stage during the next clock period.
U.S. Pat. No. 4,766,564, also to DeGroot, is directed to a data processing system which includes multiple floating point arithmetic units such as an adder and a multiplier, two putaway busses and two bypass busses connected to a register file and waiting stages associated with the arithmetic units, respectively. A special source register is included for keeping track of the source of any result in the busses so that the registers may be connected to the appropriate bus on which the result is to appear in the course of a busy or mark bit set in each register in the file and in the waiting stage. As a result, multiple data items to exit the pipes during any cycle is permitted.
It is an object of this invention to provide a floating point processor which provides for the pipelining of arithmetic operations performed by the processor.
It is another object of this invention to provide a floating point processor which provides for the pipelining of simple and compound arithmetic operations through floating point arithmetic operation units associated with the floating point processor.
It is yet another object of this invention to provide a floating point processor which includes at least one floating point arithmetic operation unit, means for pipelining input operands supplied to each arithmetic operation unit and means for pipelining results produced by each arithmetic operation unit.
It is still yet another object of this invention to provide a floating point processor which includes a plurality of floating point arithmetic operation units sharing common normalizing, denormalizing and rounding units.